Editing Ephemeris time (section)

==Definition (1952)==
Ephemeris time was defined in principle by the orbital motion of the Earth around the Sun<ref name=ESAAp79 /> (but its practical implementation was usually achieved in another way, see below). Its detailed definition was based on [[Simon Newcomb]]'s [[Newcomb's Tables of the Sun|''Tables of the Sun'']] (1895),<ref name="NewcSun" /> implemented in a new way to accommodate certain observed discrepancies:

In the introduction to ''Tables of the Sun,'' the basis of the tables (p.&nbsp;9) includes a formula for the Sun's [[mean longitude]] at a time, indicated by interval T (in units of Julian centuries of 36525 mean solar days<ref>The unit of ''mean solar'' day is left implicit on p. 9 but made explicit on p. 20 of [[#refNewcSun|Newcomb (1895)]].</ref>), reckoned from Greenwich Mean Noon on 0 January 1900:

: Ls = 279° 41' 48".04 + 129,602,768".13T +1".089T<sup>2</sup> . . . . . (1)

Spencer Jones' work of 1939<ref name="HSJ1939" /> showed that differences between the observed positions of the Sun and the predicted positions given by Newcomb's formula demonstrated the need for the following correction to the formula:

: &Delta;Ls = + 1".00  + 2".97T  + 1".23T<sup>2</sup>  + 0.0748B

where "the times of observation are in Universal time, not corrected to Newtonian time," and 0.0748B represents an irregular fluctuation calculated from lunar observations.<ref name=Clem1948-172>[[#refClem1948|Clemence (1948)]], p. 172, following [[#refHSJ1939|Spencer Jones (1939)]].</ref>

Thus, a conventionally corrected form of Newcomb's formula, incorporating the corrections on the basis of mean solar time, would be the sum of the two preceding expressions:

: Ls =	279° 41' 49".04 + 129,602,771".10T +2".32T<sup>2</sup> +0.0748B . . . . . (2)

Clemence's 1948 proposal, however, did not adopt such a correction of mean solar time. Instead, the same numbers were used as in Newcomb's original uncorrected formula (1), but now applied somewhat prescriptively, to define a new time and time scale implicitly, based on the real position of the Sun:

: Ls =	279° 41' 48".04 + 129,602,768".13E +1".089E<sup>2</sup> . . . . . (3)

With this reapplication, the time variable, now given as E, represents time in ephemeris centuries of 36525 '''ephemeris days''' of 86400 '''ephemeris seconds''' each.  The 1961 official reference summarized the concept as such: "The origin and rate of ephemeris time are defined to make the Sun's mean longitude agree with Newcomb's expression"<ref>[[#refESAE|ESAE (1961)]] at p. 70.</ref>

From the comparison of formulae (2) and (3), both of which express the same real solar motion in the same real time but defined on separate time scales, Clemence arrived at an explicit expression, estimating the difference in seconds of time between ephemeris time and mean solar time, in the sense (ET-UT):

<math> \delta t = +24^s.349 + 72^s.3165T +29^s.949T^2 + 1.821B</math> . . . . . (4)<ref name="Clem1948-172" />

with the 24.349 seconds of time corresponding to the 1.00" in ΔLs.
Clemence's formula (today superseded by more modern estimations) was included in the original conference decision on ephemeris time. In view of the fluctuation term, practical determination of the difference between ephemeris time and UT depended on observation.  Inspection of the formulae above shows that the (ideally constant) units of ephemeris time have been, for the whole of the twentieth century, very slightly shorter than the corresponding (but not precisely constant) units of mean solar time (which, besides their irregular fluctuations, tend to lengthen gradually). This finding is consistent with the modern results of Morrison and Stephenson<ref name="morr3">[[#morrste2004|L V Morrison & F R Stephenson (2004)]]; also [[#stemorr84|F R Stephenson, L V Morrison (1984)]], and [[#stemorr95|F R Stephenson, L V Morrison (1995)]].</ref> (see article [[ΔT (timekeeping)|&Delta;T]]).